Boolean Logic Flashcards

These flashcards cover the fundamental concepts of Boolean logic, including operators, truth tables, logic gates, and simplification techniques.

What are the fundamental binary logical operators?

AND, OR, NOT, and XOR

What are alternative notations for AND, OR, NOT, and XOR?

AND: ⋅ or ⋀ or ; OR: + or ⋁; NOT: ' or ˉ or ¬; XOR: ⊕

How are NAND and NOR operations defined in terms of AND, OR, and NOT?

A NAND B = (A AND B)'; A NOR B = (A OR B)'

Why are NAND and NOR gates considered 'universal'?

Any binary logic circuit can be built entirely from NAND gates, or from NOR gates.

What can we use to build computer logic?

Vacuum Tubes, Relays, Transistors, etc.

State de Morgan's Law.

(AB)’ = A’ + B’; (A + B)’ = A’B’

What is the basic approach to designing logic circuits?

1. Write out a truth table. 2. Derive a Boolean expression in sum-of-products form. 3. Translate the Boolean expression to logic gates.

What is the sum-of-products form of the stair-hall lighting circuit (XOR)?

L = S’H + SH’

What is the inverted AND form of the multiplexer's Boolean Expression?

( (AC1’C2’)’ (BC1’C2)’ (CC1C2’)’ (DC1C2)’ )’

What is the purpose of Karnaugh maps (K-maps)?

Offer an easy way to minimise a Boolean function to produce a functionally equivalent, but simpler, implementation.

What is a Karnaugh map (K-map)?

A grid in which each square represents one possible combination of inputs, ordered so that only one input changes from col-to-col, and from row-to-row.

How to restate an expression that is ANDed or ORed together using DeMorgan's Law?

by negating the overall expression, negating the sub-expressions, and flipping the operators from OR to AND, or vice versa